Homogenization Approach for the Limit Analysis of Out-of-Plane Loaded Masonry Walls
Publication: Journal of Structural Engineering
Volume 132, Issue 10
Abstract
This paper addresses the usage of a simplified homogenization technique for the analysis of masonry subjected to out-of-plane loading. The anisotropic failure surface, based on the definition of a polynomial representation of the stress tensor components in a finite number of subdomains, is combined with finite element triangular elements employed for the upper and lower bound limit analyses. Several comparisons between the proposed model and experimental data available in the literature are presented, for wallettes subjected to bending at different orientations and for different panels loaded out of plane. The limit analysis results allow us to identify the distribution of internal forces at critical sections and to obtain the collapse modes, as well as the failure loads. Excellent results are found in all cases, indicating that the proposed simple tool is adequate for the safety assessment of out-of-plane loaded masonry panels. The combined usage of upper and lower bound approaches, and their respective simplifications, allow us to define a narrow interval for the real collapse load.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Two of the writers, A. Tralli and G. Milani, gratefully acknowledge the support of the research project MIUR Grant No. MUIRCOFIN 2003—Interfacial damage failure in structural systems, coordinator: Professor A. Tralli.
References
Anderheggen, E., and Knopfel, H., (1972). “Finite element limit analysis using linear programming.” Int. J. Solids Struct., 8, 1413–1431.
Belytschko, T., and Hodge, P. G. (1970). “Plane stress limit analysis by finite elements.” J. Engrg. Mech. Div., 96(6), 931–944.
British Standard Institution. (2002). “Code of practice for use of masonry. Structural use of unreinforced masonry.” BS 5628–1:1992, London.
Cannarozzi, A. A., Capurso, M., and Laudiero F. (1978). “An iterative procedure for collapse analysis of reinforced concrete plates.” Comput. Methods Appl. Mech. Eng., 16, 47–68.
Cannarozzi, A. A., Sacchi, P. L., and Tralli, A. (1982). “On the limit analysis of steel structures in presence of shear.” J. Mecanique Theorique Appliquee, 1(3), 379–401.
Chong, V. L., Southcombe, C., and May, I. M. (1994). “The behaviour of laterally loaded masonry panels with openings.” Proc., 3rd Int. Masonry Conf., Proc. British Masonry Society, London, 178–182.
European Committee for Standardization (CEN) (2004), “Design of masonry structures. Common rules for reinforced and unreinforced masonry structures.” EN 1996-1-1:2002, Eurocode 6, Brussels, Belgium.
Gazzola, E. A., and Drysdale, R. G. (1986). “A component failure criterion for blockwork in flexure.” Proc., Structures ‘86 ASCE, S. C. Anand, ed., New Orleans, 134–153.
Gazzola, E. A., Drysdale, R. G., and Essawy, A. S. (1985). “Bending of concrete masonry walls at different angles to the bed joints.” Proc., 3rd North. American Mas. Conf., Arlington, Tex., Paper 27.
Hellan, K. (1967). “Analysis of elastic plates in flexure by a simplified finite element method.” Acta Polytech. Scand., 46, 1–28.
Herrmann, L. R. (1967). “Finite element bending analysis for plates.” J. Engrg. Mech. Div., 93, 13–26.
Hodge, P. G. (1959). Plastic analysis of structures, McGraw-Hill, New York.
Krabbenhoft, K., and Damkilde, L. (2002). “Lower bound limit analysis of slabs with nonlinear yield criteria.” Comput. Struct., 80, 2043–2057.
Krabbenhoft, K., and Damkilde, L. (2003). “A general nonlinear optimization algorithm for lower bound limit analysis.” Int. J. Numer. Methods Eng., 56, 165–184.
Krenk, S., Damkilde, L., and Hyer, O. (1994). “Limit analysis and optimal design of plates with equilibrium elements.” J. Eng. Mech., 120(6), 1237–1254.
Lourenço, P. B. (1997). “An anisotropic macro-model for masonry plates and shells: Implementation and validation.” Rep. No. 03.21.1.3.07, Univ. of Delft, Delft, Holland and Univ. of Minho, Guimarães, Portugal. www.civil.uminho.pt/masonry.
Lourenço, P. B. (2000). “Anisotropic softening model for masonry plates and shells.” J. Struct. Eng., 126(9), 1008–1016.
Maier, G. (1977). “Mathematical programming methods for deformation analysis at plastic collapse.” Comput. Struct., 7, 599–612.
Milani, G., Lourenço, P. B., and Tralli, A. (2005). “Homogenised limit analysis of masonry walls. Part I: Failure surfaces.” Comput. Struct., 84(3-4), 166–180.
Munro, J., and Da Fonseca, A. M. A. (1978). “Yield-line method by finite elements and linear programming.” Struct. Eng., 56B, 37–44.
Sinha, B. P. (1978). “A simplified ultimate load analysis of laterally loaded model orthotropic brickwork panels of low tensile strength.” Struct. Eng., 56B(4), 81–84.
Sloan, S. W. (1988). “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Analyt. Meth. Geomech., 12, 61–67.
Southcombe, C., May, I. M., and Chong, V. L. (1995). “The behaviour of brickwork panels with openings under lateral load.” Proc., 4th Int. Masonry Conf. Proc., British Masonry Society, Vol. 1, London, 105–110.
Spence, R., and Coburn, A. (1992). “Strengthening building of stone masonry to resist earthquakes.” Meccanica, 27, 213–221.
Suquet, P. (1983). “Analyse limite et homogeneisation.” C. R. Seances Acad. Sci., Ser. 2, 296, 1355–1358.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 132 • Issue 10 • October 2006
Pages: 1650 - 1663
Copyright
© 2006 ASCE.
History
Received: Jul 8, 2005
Accepted: Nov 29, 2005
Published online: Oct 1, 2006
Published in print: Oct 2006
Notes
Note. Associate Editor: Elisa D. Sotelino
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.